The pKa_s of titratable groups in proteins, or rather the shifts relative to the pKa_s of single aminoacids in solution, are indicators of the local electrostatic environment of the group and sensitive also to the global structure of the protein. Their prediction requires a good understanding of the electrostatic interactions between the protein and the (aqueous) solvent, as well as of the intramolecular interactions. So far the theoretical predictions have included both the structure of the solvent and the dynamics of the protein in minimal way by the use of dielectric constants that differ from unity. These so-called continuum models allow for a much larger simulation box than those in use in molecular dynamics codes, thus improving the treatment of the long distance electrostatic interactions. They suffer, however, from a drawback: effects associated with the first few salvation shells are not taken into account. Whether the long distance or the first solvation shells are more important in determining the pKa_s shifts (as well as other electrostatic properties) is still in debate, and the answer probably depends on the position of the titratable group as well as the structure of the protein. We have computed the pKa_s of titratable groups in lysozyme from simulations with explicit solvent. This protein has been chosen for several reasons: (a) there is a wealth of experimental information regarding its ionizable groups as well as from Poisson-Boltzmann calculations, (b) it has a relatively large number (21) of titratable groups, which we expect will allow us to correlate the pKa shifts with position and relative distance between groups. The calculations to date have encountered some serious difficulties, and we are in the process of attempting to improve the results.